Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
150 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C79 | #1409 |
| commutator | C4×C8 | C2×C4×C79 |
| Frattini, cosocle | #492 | C22×C79 |
| prime radical | #127×C79 | D4 |
| LCS | G ▷ C4×C8 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C79 ◁ C22×C79 ◁ C2×C4×C79 ◁ C42×C79 ◁ #492×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #498×C79 | C4 | semidirect |
| 10. C82×C79 | C4 | semidirect |
| 57. #7535 | C79 | direct (N × H) |
| 64. C79 | #7535 | direct (N × H) |
| 66. #498 | C4×C79 | semidirect |
| 71. C82 | C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C79×#1705 | 2 |
| C79×#1410 | 2 |
| C79×#1409 | 2 |
| #7535 | 79 |